Suppose that $f(x,y)$ is a smooth function and that its partial derivatives have the values, $f_x(0, 9) = -4$ and $f_y(0, 9) = -2$. Given that $f(0, 9) = 1$, use this information to estimate the value of $f(1, 10)$. Note this is analogous to finding the tangent line approximation to a function of one variable. In fancy terms, it is the first Taylor approximation.
Estimate of (integer value) $f(0, 10)$
Estimate of (integer value) $f(1, 9)$
Estimate of (integer value) $f(1, 10)$